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Abstract

We explore the passive optical sorting of plasmon nanoparticles and investigate the optimal wavelength and optimal beam shape of incident field. The condition for optimal wavelength is found by maximising the nanoparticle separation whilst minimising the temperature increase in the system. We then use the force optical eigenmode (FOEi) method to find the beam shape of incident electromagnetic field, maximising the force difference between plasmon nanoparticles. The maximum force difference is found with respect to the whole sorting region. The combination of wavelength and beam shape study is demonstrated for a specific case of gold nanoparticles of radius 40nm and 50nm respectively. The optimum wavelength for this particular situation is found to be above 700nm. The optimum beam shape depends upon the size of sorting region and ranges from plane-wave illumination for infinite sorting region to a field maximising gradient force difference in a single point.

Figures (7)

a) Scattering Qsca and absorption Qabs efficiencies calculated using Mie theory for 3D nanoparticle of r1 = 50nm and the corresponding 2D values converted to 3D equivalents. Nanoparticle is in water with nw = 1.33; b) Forces and their respective difference ΔF acting on r1 = 50nm and r2 = 40nm gold nanoparticles. Forces are parallel to the substrate plane. The illumination is a plane-wave at near critical angle of θ = 64° with power density corresponding to 1mW/μm2; c) Speed difference Δv and temperature increase ΔT for the same illumination as in b); d) Speed difference normalised with respect to the temperature increase in the system.

Field optimising the force difference ΔF for gold nanoparticles of radius r1 = 50nm and r2 = 40nm in a single point x = 0 with corresponding amplitude |aμ| and phase arg(aμ) for each plane wave from angular spectrum. The |aμ| and arg(aμ) correspond to the pattern at the back focal plane of the objective. This illumination of the back focal plane forms a very strong field gradient in +x direction in the focal plane, which maximises the force difference for our testing particles. Note that scattering from the particles is not included.

Field optimising the force difference ΔF for l = 500nm. The phase of aμ is plotted in the region where it is well-defined. Notice that the field is focused into the ROI. The left edge of the back focal plane contributes the most to the optimised field in the focal plane. The phase at the back focal plane is slightly modulated as well.

Field optimising the force difference ΔF for l → 100mm. As the phase of aμ for zero amplitude |aμ| is not well defined, it is not displayed in the graph. The optimum angle plane wave is 64°, which is close to critical angle for given interface.

(a) Blue and green points show forces acting on individual particles in optimised field for l = 500nm. Red points show the force difference. The coloured lines show the same but for plane wave illumination optimising the infinite system. (b) The ratio ΔF/ΔFpw as a function of ROI size. The dip around l = 14μm is due to k-space discretization of angular spectrum representation. The gain in ΔF is significant in the experimentally interesting region.